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Chapter 5: Problem 12

How many kcal will it take to heat 1 liter of water (e.g., in a pot) from room temperature \(\left(20^{\circ} \mathrm{C}\right)\) to boiling \(\left(100^{\circ} \mathrm{C}\right) ?\) How many Joules is this?

Short Answer

Expert verified
Answer: It takes 80 kcal or 334720 Joules to heat 1 liter of water from room temperature to boiling.

Step by step solution

01

Identify the given information

We are given: - Initial temperature: \(20^{\circ} \mathrm{C}\) - Final temperature: \(100^{\circ} \mathrm{C}\) - Volume of water: 1 liter = 1000 g (since the density of water is 1 g/mL) - Specific heat capacity of water: \(4.18 \frac{\mathrm{kJ}}{\mathrm{kg\cdot K}} = 1.00 \frac{\mathrm{kcal}}{\mathrm{kg\cdot K}}\)
02

Calculate the temperature difference

Delta T, or the change in temperature, is the difference between the final temperature and the initial temperature: \(\Delta T = (100 - 20)^{\circ} \mathrm{C} = 80^{\circ} \mathrm{C}\)
03

Calculate the energy required in kcal

To find the energy required to heat the water, use the formula: \(Q = mc\Delta T\) Where - \(Q\) is the energy required - \(m\) is the mass of the substance (1 kg, since 1000 g = 1 kg) - \(c\) is the specific heat capacity (1.00 \(\frac{\mathrm{kcal}}{\mathrm{kg\cdot K}}\)) - \(\Delta T\) is the change in temperature (80 \(^{\circ}\mathrm{C}\)) Plug in the values: \(Q = (1\,\mathrm{kg})\times(1.00\,\frac{\mathrm{kcal}}{\mathrm{kg\cdot K}})\times(80\,\mathrm{K})\) \(Q = 80\,\mathrm{kcal}\) It takes 80 kcal to heat 1 liter of water from room temperature to boiling.
04

Convert kcal to Joules

To convert 80 kcal to Joules, use the conversion factor: 1 kcal equals to 4184 Joules \(80\,\mathrm{kcal} \times \frac{4184\,\mathrm{J}}{1\,\mathrm{kcal}} = 334720\,\mathrm{J}\) It takes 334720 Joules to heat 1 liter of water from room temperature to boiling.

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Most popular questions from this chapter

Considering the typical wavelength of light to be \(0.55 \mu \mathrm{m}\), what is a typical photon energy, in Joules, and how many photons per second emerge from a \(1 \mathrm{~W}\) light source? \(^{54}\)

A smaller or less active person may require only \(1,300 \mathrm{kcal}\) per day of food intake, while a larger or more active person might demand \(3,000 \mathrm{kcal}\) per day. Approximately what range of power does this spread translate to, in Watts?

A car headlight using light emitting diodes (LEDs) operates at about \(15 \mathrm{~W}\). If drawing from the car's \(12 \mathrm{~V}\) battery, how much current, in Amps, flows to the headlight?

A generic \(\$ 10\) pizza might contain about \(2,500 \mathrm{kcal}\). What is this in \(\mathrm{kWh}\) ? Electricity typically costs \(\$ 0.15\) per \(\mathrm{kWh},{ }^{44}\) so how much would a pizza's amount of energy cost in electrical terms? Which of the two is a cheaper form of energy?

A \(50 \mathrm{~kg}\) crate might require \(200 \mathrm{~N}\) to slide across a concrete floor. If we must slide it \(10 \mathrm{~m}\) along the floor and then lift it \(2 \mathrm{~m}\) into a truck, how much energy goes into each action, and what fraction of the total energy expenditure is each?
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